WS8Key - hdath.224,Sprnng2007\Norksheet8 3 t Use the front...

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Unformatted text preview: hdath.224,Sprnng2007.\Norksheet8 3% t Use the front and back of this sheet to complete the following problems. If additional paper is needed, staple the extra sheet to this one. Name: 1. Solve problem #8 in text section 5.3. ~ _ _ 3 2 2. For the system { and L(x,y) : (1x2 -I— by2 (a) Show from the following that for one set of parameters L a Lyapunov function and for the other it isn’t. (Can you come up with a general relationship between the parameters such that L will be a Lyapunov function?) ia:&b:2 itazrb=i (b) Draw the level curves for L for the case Where it is a Lyapunov function. 3. Solve problem #18 in text section 4.1. fl i ~' - V‘v‘xm \ ill: \/ ,. ‘m t) X} key... A r ,f M <3 M“ X‘ g M X7 w9_6if\“’<i kWh 2,.“ a l‘ n if E C "gwf aka) \(A Mi Q 3 «M5 2'15 :2) a {M W0 (“1:3 as; " in; \lmv‘fi” V3 ‘3 P ’“N \ N D A, “(hum WNW.“ m ‘\’~«~z:5~'wa 5* \ (way; i: \g (*qufifi- m “Lab l MK” Q 7;» Q4? rm 5m w ,cm W + E1 1 M ’\/ \R L, , u m we: \/ V} 23:; *- : / Lfl A (W \ Y? L’\ TL; %' \ ‘ é: / ,. W a W “5 Wm“ ' a i; \f{3;>>1 Q :1” m L K; %* {Mi 4; g “’76) h_’_ _ M ,WW,MW M mmfit ’ (M {3% w «1 Cm; Wt ré WI” gm “NJ + gm ’I \f m {3: am 42(1) m «2% m hm QM“ L \ 75 h 3 j i .. , W“ W § k5. \1 (f: 5% , ,1 E 2 t (A W1 (:2; am wkfia, 9:: W 3k: $m$xfha%“kgfiég::®&mmg $%\xfi%Q&m€%kwkfi%fl& “0% bgfifi, (3a,. « “A a“ 513%,. ‘ SN?» UL iii-UK,“ Q4“ ...
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This homework help was uploaded on 04/08/2008 for the course MATH 224 taught by Professor Hahn during the Spring '07 term at Case Western.

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WS8Key - hdath.224,Sprnng2007\Norksheet8 3 t Use the front...

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